4 x 4 x 8 Tri-dimensional Chess

written by Alberto Monteiro

Origins

This game was probably developed by my cousin Silvio Levy in 1980, with
whom I played some games until we decided upon a minor change. Since
then, I have played it with Carlos Seiblitz and
with Oscar Luiz Vieira Ferreira.

However, the advance of the game is so slow, that in the c. 20 games I
played, I never gave a checkmate to anyone; all the games either
finished by being suspended, or by the opponent's resignation.

The Board

The Board is composed of four 4 x 8 chessboards placed one over the
other. Silvio had build a nice 3-D set once, but we usually played in
common boards, imagining the 3-D display.

The game has rotational symmetry: if the King, Queen, and the
King's Pawn are coplanar, so are the King, King's Knight and King's
Pawn. In other words, the game would be exactly the same if, instead of
the design, above, the columns were placed in the order (a,e,i,m),
(b,f,j,n), (c,g,k,o), (d,h,l,p).

Movement

In the earlier version, all Orthochess pieces would move like
Orthochess, with the generic interpretation of the plane of its
movement. For example, a Knight at b1 might choose to move in the
(a,b,c,d) x (1-8) plane, to a3, c3 or d2; or in the (b,f,j,n) x (1-8)
plane, to f3 or j2; or in the (a,b,c,d) x (b,f,j,n) plane, to h1, i1 or
k1.

The exceptions were the Cardinal. (In Raumschach,
or 5x5x5 Variant, this piece is the Unicorn), that would move in
the long diagonals (example: a1 - f2 - k3 - p4), and the King and Queen,
that would also get long-diagonal movements.

But, since the Cardinal would only control 1/4 of the squares, we
decided to change the movements of the Cardinal for those of the Bishop.
In this way, each one of the four bishops would control 1/4 of the
squares, so that they, together, would control the whole board (it might
even be possible to checkmate with K + B + B + B + B vs K).

(Afterthought: it would be more correct to change the display, replacing
the B[ishop] by U[nicorn], and the C[ardinal] by B[ishop]...)

Notice that this game has potential for increasing, with some natural
pieces, like two 3D Knights (1,1,2) or (1,2,2) or a 3D Pawn (fcTfmW)

Strategies

It's very hard to give checkmate to the opposite King: a King in the
center of the board can move to 26 different squares! Even if the King
is cornered to a1 (or d1, m1, p1, a8, etc), there would still be 7 extra
squares. A checkmate with K + R vs K is impossible.

So, the winning strategy is capture the other pieces, promote pawns to
Queens, and, with massive material advantage, mate the King.

Since we are bound to 2D thinking, the Bishops become very powerful
pieces, as soon as they are brought to the attack. The normal way of
developing them is by fianchetto: b3 - B(e1)b2 - B(b2)l4, with pressure
over g5 and b6; or by the central squares: j3 - B(e1)o3 or j3 - B(e1)j2
- B(j2)m3!. The Bishops are stronger when they are in the (a), (d), (m)
or (p) columns, when they have maximum range.

The Knights are also very powerful (in an unbound board, each Knight
would control 3! * 2 * 2 = 24 squares), and can be coordinated to
assault the opponent's weak pawns. Since the limitations of the Board
restrain the diagonal movements, the slowness of the Orthoknight is not
inherited to 3D: the Knight is probably much stronger then the Cardinal,
the Bishop and, maybe, the Rook.

Comments

Further to my previous comments I have now devised better names for my suggested combined pieces. I was particularly dissatisfied with Spire - 'a tower-like building with a horn-like top'. As part of a more comprehensive set of names I have settled on DUCHESS for the rook-unicorn combination and GOVERNOR for the bishop-unicorn one.

Further to my previous coment, all reference to 'files' should of course read 'ranks'. The file is of course the same 8-cell line as in standard 2-d chess, except there are 16 of them. It is easy to get confused in 3 dimensions!

This is the best 3-d game I have seen so far on these pages. By being even in every dimension it overcomes the problem in Raumschach of unequal squares of different colours. It has much in common with a version that I devised, which also uses a 4-by-4 'file' with the second full of pawns and rooks at the corners of the first. My pattern for the first file was RUBR BEQU USMB RBUR where E represents an EMPEROR - a king which can also move one square on the TRIAGONAL - C a SPIRE combining rook and unicorn moves - and M a MINOTAUR combining bishop and unicorn moves. Names in capitals are my own coinage. The author's suggestion of modifying to have 4 unicorns and 2 bishops is a good one, and gives me an idea for combining the best of both our versions by having unicorns along two sides and a bishop and knight along the others, thus RUUR BEQB NSMN RUUR.